1. Field of the Invention
The present invention relates generally to a wireless communication system, and in particular, to a transmitting and receiving apparatus using transmit antenna diversity to combat the degradation effects of fading.
2. Description of the Related Art
One of effective techniques to mitigate fading is transmit diversity in a wireless communication system. Assuming that the channel characteristics of a receiver are known to a transmitter, a switched diversity technique has been proposed (J. H. Winters “Switched Diversity with Feedback for DPSK Mobile Radio System”, IEEE Trans. Veh. Technol., vol. 32, pp. 134-150, February 1983) and a multivibrate modulation/coding has also been proposed (G. G. Raleigh and V. K. Jones, “Multivibrate Modulation and Coding for Wireless Communication”, IEEE J. Select. Areas. Commun., vol. 17, pp. 851-866, May 1999).
In practice, however, it is nearly impossible for the transmitter to have perfect instantaneous information about the characteristics of the receiver because of mobility and channel changes. Also, the use of feedback channels for reporting channel status information to the transmitter may not be desirable since it reduces channel capacity. Thus, many researchers have focused on the transmit diversity scheme assuming that the transmitter does not know channel information. An initial type of transmit diversity scheme was proposed by Wittneben (A. Wittneben, “Base Station Modulation Diversity for Digital SIMULCAST”, in proc. IEEE'VTC, May 1993, pp. 505-511). Foschini studied layered space-time architectures for multiple transmit antenna systems (G. J. Foschini, Jr., “Layered Space-Time Architecture for Wireless Communications in a Fading Environment When Using Multi-element Antennas”, Bell Labs Tech. J., pp. 41-59, Autumn 1996). In the presence of Gaussian Noise, Telatar analyzed the capacity of multiple antenna systems (E. Telatar, “Capacity of Multi-Antenna Gaussian Channels”, AT&T-Bell Laboratories, Internal Tech. Memo., June 1995). Later, Foschini et. al. derived the expression of outage capacity under the assumption of quasi-static fading (G. J. Foschini, Jr. and M. J. Gans, “On Limits of Wireless Communication in a Fading Environment When Using Multiple Antennas”, Wireless Personal Commun., vol. 6, pp. 311-335, 1998).
Recently, space-time coding has received increased attention due to its good performance for high-rate transmissions. Tarokh et. al. introduced space-time trellis coding that provides both coding gain and diversity gain (V. Tarokh, N. Seshadri, and A. R. Calderbanck, “Space-Time Codes for High Data Rate Wireless Communications: Performance Criterion and Code Construction”, IEEE Trans. Inform. Theory, vol. 44, pp. 744-765, March 1998, and V. Tarokh, N. Seshadri, and A. R. Calderbanck, “Space-Time Codes for High Data Rate Wireless Communications: Performance Criteria in the Presence of Channel Estimation Errors, Mobility, and Multiple Paths”, IEEE Trans. Inform. Theory, vol. 47, pp. 199-207, February 1999). Particularly, the space-time trellis coding disclosed in the second thesis of Tarokh offers the best possible trade-off between constellation size, data rate, diversity advantage, and trellis complexity.
However, according to the above space-time coding techniques, the decoding complexity increases exponentially with transmission rate when the number of transmit antennas is fixed. Therefore, they are not feasible for a large of transmit antennas and at a high bandwidth efficiency.
To overcome this problem, Alamouti and Tarokh proposed space-time block coding (S. M. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communications”, IEEE J. Select Areas Commun., vol. 16, pp. 1451-1458, October 1998 and V. Tarokh, H. Jafarkhani, and A. R. Calderbandk, “Space-Time Block Codes from Orthogonal Designs”, IEEE Trans. Inform. Theory, vol. 45, pp. 1456-1467, July 1999). These space-time block codes introduce temporal/spatial correlation into signals transmitted from different transmit antennas, so as to provide diversity gain at the receiver and coding gain over an uncoded system. Despite the advantage of simple transmission/reception, these codes cannot achieve all possible diversity gains without data rate losses when complex symbols are transmitted through 3 or more antennas, due to the orthogonality condition for the columns of a transmission matrix.
FIG. 1 is a block diagram of a transmitter using conventional space-time block coding. Referring to FIG. 1, the transmitter is comprised of a serial-to-parallel (S/P) converter 10, an encoder 20, and N transmit antennas 30-1 to 30-N. The S/P converter 10 groups every N symbols received from an information source (not shown) into a block. The encoder 20 generates a predetermined number of symbol combinations from the N symbols and feeds them to the N transmit antennas 30-1 to 30-N for corresponding time periods.
FIG. 2 is a block diagram of a receiver that receives signals from the transmitter illustrated in FIG. 1. Referring to FIG. 2, the receiver is comprised of M receive antennas 40-1 to 40-M, a channel estimator 50, a multi-channel symbol arranger 60, and a decoder 70. The channel estimator 50 estimates channel coefficients representing channel gains from the transmit antennas 30-1 to 30-N to the receive antennas 40-1 to 40-M. The multi-channel symbol arranger 60 collects symbols received from the receive antennas 40-1 to 40-M. The decoder 70 achieves a desired result by multiplying the symbols received from the multi-channel symbol arranger 60 by the channel coefficients, computes decision statistic for all possible symbols using the result, and detects desired symbols through threshold detection.
In a communication system configured as illustrated in FIGS. 1 and 2, let ci,t be the symbol transmitted from transmit antenna i at time t and ai,j be the channel gain from transmit antenna i to receive antenna j. Then the signal ri,j received at receive antenna j at time t is given by equation (1):
                              r                      t            ,            j                          =                                            ∑                              k                =                1                            K                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                                                a                                      i                    ,                    j                                                  ⁢                                  c                                      i                    ,                    t                                                                                +                      n                          t              ,              j                                                          (        1        )            where k is a time index within each time period and nt,j is the noise for the channel between transmit antennas and receive antenna j at time t.
Assuming signals transmitted from different transmit antennas undergo independent Rayleigh fades, the channel gains ai,j are modeled as samples of independent complex Gaussian random variables with zero mean and variance of 0.5 per dimension and the noise values nt,j are modeled as samples of independent complex Gaussian random variables with zero mean and variance of No/2 per dimension, where No is the noise spectral density.
An optimum space-time block code is designed so as to maximize the minimum coding gain of an error matrix. The error matrix refers to a matrix of the differences between original symbols and erroneous symbols arranged in the receiver, and the minimum coding gain is the product of the eigen values of the error matrix.
For illustration, it is assumed that there are 2 transmit antennas and M receive antennas. The transmitter maps b input bits to one of 2b complex symbols using a signal constellation with 2b elements. At a first time period, 2b bits arrive at the encoder and constellation symbols s1 and s2 are picked up. The two symbols are formed with these constellation symbols and transmitted through the 2 transmit antennas for two time periods. The 2×2 transmission matrix is then shown in equation (2):
                    S        =                  (                                                                      s                  1                                                                              s                  2                                                                                                      -                                      s                    2                    *                                                                                                s                  1                  *                                                              )                                    (        2        )            where si* denotes the conjugate of si.
More specifically, the rows in the transmission matrix indicate symbols transmitted at the same time and the columns indicate symbols transmitted from the same antenna. Thus, s1 is transmitted from the first transmit antenna and s2 from the second transmit antenna at time t, and −s2* is transmitted from the first antenna and s1* from the second antenna at time t+1. This is the so-called Alamouti scheme and is an example of space-time block code.
Maximum likelihood (ML) decoding of the above space-time block code amounts to minimization of the decision metric of equation (3):
                                          ∑                          m              =              1                                M                ⁢                  (                                                                                                          r                                          1                      ,                      m                                                        -                                                            a                                              1                        ,                        m                                                              ⁢                                          s                      1                                                        -                                                            a                                              2                        ,                        m                                                              ⁢                                          s                      2                                                                                                  2                        +                                                                                                                      a                                              1                        ,                        m                                                              ⁢                                          s                      2                      *                                                        -                                                            a                                              2                        ,                        m                                                              ⁢                                          s                      1                      *                                                                                                  2                                )                                    (        3        )            over all possible symbol pairs of s1 and s2. It can be shown that the above metric decomposes into two parts, shown as equation (4), one of which
                              -                                                    ∑                                  m                  =                  1                                            M                        ⁢                          [                                                                    r                                          1                      ,                      m                                                        ⁢                                      a                                          1                      ,                      m                                        *                                    ⁢                                      s                    1                    *                                                  +                                                      r                                          1                      ,                      m                                        *                                    ⁢                                      a                                          1                      ,                      m                                                        ⁢                                      s                    1                                                  +                                                      r                                          2                      ,                      m                                                        ⁢                                      a                                          2                      ,                      m                                        *                                    ⁢                                      s                    1                                                  +                                                      r                                          2                      ,                      m                                        *                                    ⁢                                      a                                          2                      ,                      m                                                        ⁢                                      s                    1                    *                                                              ]                                      +                                                                          s                1                                                    2                    ⁢                                                    ∑                                  m                  =                  1                                            M                        ⁢                                                            ∑                                      n                    =                    1                                                  2                            ⁢                                                                                      a                                          n                      ,                      m                                                                                        2                                                                                    is only a function of s1. And the other one
                              -                                                    ∑                                  m                  =                  1                                            M                        ⁢                          [                                                                    r                                          1                      ,                      m                                                        ⁢                                      a                                          2                      ,                      m                                        *                                    ⁢                                      s                    2                    *                                                  +                                                      r                                          1                      ,                      m                                        *                                    ⁢                                      a                                          2                      ,                      m                                                        ⁢                                      s                    2                                                  -                                                      r                                          2                      ,                      m                                                        ⁢                                      a                                          1                      ,                      m                                        *                                    ⁢                                      s                    2                                                  -                                                      r                                          2                      ,                      m                                        *                                    ⁢                                      a                                          1                      ,                      m                                                        ⁢                                      s                    2                    *                                                              ]                                      +                                                                          s                2                                                    2                    ⁢                                                    ∑                                  m                  =                  1                                            M                        ⁢                                                            ∑                                      n                    =                    1                                                  2                            ⁢                                                                                      a                                          n                      ,                      m                                                                                        2                                                                        (        4        )            is only a function of s2. Minimizing Eq. (3) is equivalent to minimizing the two metric parts in Eq. (4) because the two metric parts are independent of each other. Thus, the decoder design is simplified by decoding s1 and s2 respectively with the minimized two metric parts.
Eliminating non-symbol related parts from the metric parts, the ML decoding is equivalent to minimizing the metrics of equation (5):
                                    [                                                    ∑                                  m                  =                  1                                            M                        ⁢                          (                                                                    r                                          1                      ,                      m                                                        ⁢                                      a                                          1                      ,                      m                                        *                                                  +                                                      r                                          2                      ,                      m                                        *                                    ⁢                                      a                                          2                      ,                      m                                                                                  )                                ]                -                  s          1                            2    +            (                        -          1                +                                            ∑                              m                =                1                                      M                    ⁢                                                    ∑                                  n                  =                  1                                            2                        ⁢                                                                            a                                      n                    ,                    m                                                                              2                                          )        ⁢                                    s          1                            2      for decoding s1 and
                                                                                    [                                                                            ∑                                              m                        =                        1                                                              M                                    ⁢                                      (                                                                                            r                                                      1                            ,                            m                                                                          ⁢                                                  a                                                      2                            ,                            m                                                    *                                                                    +                                                                        r                                                      2                            ,                            m                                                    *                                                ⁢                                                  a                                                      1                            ,                            m                                                                                                                )                                                  ]                            -                              s                2                                                          2                +                              (                                          -                1                            +                                                                    ∑                                          m                      =                      1                                                        M                                ⁢                                                                            ∑                                              n                        =                        1                                                              2                                    ⁢                                                                                                          a                                                  n                          ,                          m                                                                                                            2                                                                        )                    ⁢                                                                  s                2                                                    2                                              (        5        )            for decoding s2.
Thus, it is observed that space-time block coding can be implemented using a very simple coding/decoding algorithm and can also achieve 1 spatial diversity 2M, where M is the number of receive antennas. For this reason, it has been adapted by various international standardization bodies including WCDMA (Wide-band Code Division Multiple Access) and IS (International Standard)-136.
To achieve the remarkable properties of the space-time block coding, the columns of the transmission matrix must be orthogonal to each other. The above space-time block coding scheme provides a diversity order equal to the number of transmit antennas without loss in transmission rate (i.e., maximum diversity order) even if complex symbols are transmitted from 2 transmit antennas. To generalize the above scheme to more than 2 transmit antennas, a space-time block code in the form of a matrix of orthogonal columns provides a maximum diversity order. Examples of these codes are shown in equation (6):
                              (                                                                      s                  1                                                                              s                  2                                                                              s                  3                                                                                                      -                                      s                    2                    *                                                                                                s                  1                  *                                                            0                                                                                      s                  3                  *                                                            0                                                              -                                      s                    1                    *                                                                                                      0                                                              s                  3                  *                                                                              -                                      s                    2                    *                                                                                )                ⁢                  (                                                                      s                  1                                                                              s                  2                                                                              s                  3                                                            0                                                                                      -                                      s                    2                    *                                                                                                s                  1                  *                                                            0                                                              s                  3                                                                                                      s                  3                  *                                                            0                                                              -                                      s                    1                    *                                                                                                s                  2                                                                                    0                                                              s                  3                  *                                                                              -                                      s                    2                    *                                                                                                -                                      s                    1                                                                                )                                    (        6        )            
The space-time block coding techniques including the Tarokh scheme using these transmission matrixes only reduces the transmission rate of one symbol per channel in use to the transmission of 0.5 or 0.75 symbol per channel use, for more than 2 transmit antennas. This problem makes them less attractive for real wireless applications.